-6x^2-4x+54=0

Solution for -6x^2-4x+54=0 equation:

-6x^2-4x+54=0

a = -6; b = -4; c = +54;
Δ = b2-4ac
Δ = -42-4·(-6)·54
Δ = 1312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{82}}{2*-6}=\frac{4-4\sqrt{82}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{82}}{2*-6}=\frac{4+4\sqrt{82}}{-12}
$